Bionomial theorem/ question (wp)

1. Sep 27, 2011

Nelo

1. The problem statement, all variables and given/known data

For what values of k does the function f(x)= x^3 + 6x^2 +kx -4 give the same remainder when divided by x-1 and x+2?

answer, however in the booklet it says the answer is 3, why is this? what did i do wrong?

2. Relevant equations

3. The attempt at a solution

So.. i set up two equations one using f(1) and one using f(-2)

f(1)= 1 + 6 + 1k -4
f(1) = -2 +k
2 = k

f(-2) = 12 -2k
2k = 12
k= 6,

I plugged 6 and 2 into the equation of f(1) and got the same (remainder of 9)

wat am i doing wrong?

2. Sep 27, 2011

Nelo

anyone??

3. Sep 27, 2011

SammyS

Staff Emeritus
Patience !!

4. Sep 27, 2011

SammyS

Staff Emeritus
What does the remainder theorem say?

Set the two remainders equal to each other. Solve for k.

5. Sep 27, 2011

Nelo

wat? like.. 6k = 2?

6/2 = 3
k=3?

6. Sep 27, 2011

eumyang

1 + 6 - 4 = -2?

Where did the f(1) and f(-2) go???? This makes no sense. If you're supposed to get the same remainder when dividing by x - 1 and x + 2, then that means that
f(1) = f(-2).

7. Sep 27, 2011

Nelo

f(1)= 1 + 6 + 1k -4
f(1) = 7-4+1k
f(1) = 3+k
-3=k

f(-2) = (-2)^3 + 6(-2)^2 + k(-2) -4
f(-2) = 12 -2k
2k = 12
k= 6

?? what do i do now

8. Sep 27, 2011

eumyang

Again, why are you making the f(1) disappear? DON'T DO THAT!

You say
f(1) = 3 + k
and
f(-2) = 12 - 2k.

Since the remainders are supposed to be equal,
f(1) = f(-2)
so substitute with the right-hand-side of the two previous equations.

9. Sep 27, 2011

Nelo

I dont get it... substitute something thats not a full equation into the right hand side of the prev 2 eq? doesnt something have to = k inorder for me to sub it into another equation..?

How do i substitute dat

10. Sep 27, 2011

eumyang

f(1) = f(-2)
Instead of f(1), write what it equaled to.
Instead of f(-2), write what it equaled to.
That's what I meant by substituting.

11. Sep 27, 2011

Nelo

f(1) = 3 + k
and
f(-2) = 12 - 2k.

3+k = 12-2k
-9 = -3k
k= 3 ...

I see, thanks :P

12. Sep 27, 2011

SammyS

Staff Emeritus
That's exactly what I suggested you do back in post #4 .

13. Sep 27, 2011

gl bk